Measurement of the Muon Lifetime

Seungkyu Ha1, Guinyun Kim2, Hongjoo Kim2, Sehwook Lee2 Korea Univ.1, Kyungpook Natl. Univ.2

KIAS-QUC Winter School on Collider Physics December 27, 2016

University of Michigan Department of Physics 5

traversed, the original π0 is split into a factor of two more photons and electrons. As the average γ-ray energy drops below the pair creation threshold of 1 MeV, this process comes to a halt and normal ionization loss depletes the electron energies. Other particles besides pions are created in the primary cosmic ray interactions but they represent only a minor fraction of the total number or energy.

Figure 2. Schematic diagram of a cosmic ray interaction in the upper atmosphere (from Fraunfelder and Henley7).

The measured cosmic ray-induced muon flux is plotted in Figure 3. At the Earth’s surface, the rate is of the order of several hundred per square meter per second. You will be able to confirm this in the present experiment. There is a slight preponderance of positive muons as would be expected from interactions of cosmic ray protons with the protons in atomic nuclei.

Discovery of Muon

the discovery of antimatter. In fact, he shared that year’s Nobel Prize with Victor Hess, the original discoverer of cosmic rays.

Anderson discovered the existence of positrons and muons by very similar methods. He studied tracks made by various cosmic ray particles in an apparatus called a cloud chamber, under the influence of an applied magnetic field. If you have taken physics and have studied magnetic forces, you will know that a charged particle curves its path when it is influenced by a magnetic field. The direction of the curve tells whether a particle has positive or negative charge, and the radius of curvature tells the charge-to-mass ratio or Z/m for the particle. The muon was discovered when Anderson found particle tracks just like an electron but with Z/m 207 times smaller; the positron was discovered when Anderson found particle tracks just like an electron but curving in the wrong direction.

Left: Carl Anderson working on his cloud chamber. Right: A cloud chamber photograph of a cosmic ray min-shower, in which electrons and positrons curve in opposite directions.

The first paper to describe the muon’s radioactive decay was published in

the journal Nature in 1940, by a pair of scientists named Williams and Roberts. Very soon after, in 1941, the muon half-life was measured by Rasetti and co-workers and found to be t1/2 = 1.5 ± 0.3 µs. We will be measuring the muon half-life in our own experiment. We’ll see if our results match Rasetti’s from 1941!

To make the story just a little bit stranger, fast-forward to 1975. In 1975

scientists discovered a particle exactly like the electron and the muon… only heavier. This extra-heavy electron was called the tau lepton (symbol “τ”, pronounced t-“ow!”). The tau decays to a muon, and has a half-life even shorter than the muon’s. Observations of tau leptons are still rather rare, but stray muons turn out to be so common in cosmic rays that many physicists consider them more of a nuisance than anything else! That’s fortunate for us, as it gives us a free, reliable source of muons for the half-life measurement we will perform.

• name: Muon

• mass: 105.66 MeV/c2 (207 me)

• Mean life time τ: 2.19 μs

• cτ: 658.6 m

• Electric charge: -1e

• Spin: 1/2

• Antiparticle: antimuon ( μ+)

• Decay: μ- → e- νe νμ (μ+ → e+ νe νμ)

μ

Source of Muon• Interactions of protons or heliums with the nuclei of the atoms that constitute our

atmosphere (nitrogen, oxygen, argon)

• Pions, charged and neutral particles

• Pion decays to a muon and a muon neutrino

• produced 15 km in the atmosphere

• The original muon energy: ~6 GeV

• Energy loss from the production to the Earth surface: ~ 2 GeV

• Mean energy of muon at the sea level: 4 GeV

• Rate: the order of several hundred per square meter per second (~ 1 μ/10 cm2∙s)

• Time dilation (Earth frame observer), Length contraction (muon rest frame)

Vertical fluxes of cosmic rays (Particle Data Book)

24. Cosmic rays 5

15 10 5 3 2 1 0

0 200 400 600 800 10000.01

0.1

1

10

100

1000

10000

Atmospheric depth [g cm–2]

Ver

tica

l fl

ux [m

–2 s

–1 s

r–1]

Altitude (km)

µ+ + µ−

π+ + π−

e+ + e−

p + n

νµ + νµ_

Figure 24.3: Vertical fluxes of cosmic rays in the atmosphere with E > 1 GeVestimated from the nucleon flux of Eq. (24.2). The points show measurements ofnegative muons with Eµ > 1 GeV [32–36].

the intensity curve for the parent pions serves to calibrate the atmospheric νµ beam [37].Because muons typically lose almost 2 GeV in passing through the atmosphere, thecomparison near the production altitude is important for the sub-GeV range of νµ(νµ)energies.

The flux of cosmic rays through the atmosphere is described by a set of coupled cascadeequations with boundary conditions at the top of the atmosphere to match the primaryspectrum. Numerical or Monte Carlo calculations are needed to account accurately fordecay and energy-loss processes, and for the energy-dependences of the cross sections andof the primary spectral index γ. Approximate analytic solutions are, however, useful in

February 16, 2012 14:07

Experimental Setup

5” PMT

Liquid Scintillator (30x30x30 cm3)1,2,4-Trimethylbenzene +2,5-diphenyloxazole

(10%)

Mineral oil (90%)

NGT400 (charge, time)

HV (1400 V)

Readout cable

Laptop

2002 IEEE Short Course Radiation Detection and Measurement Helmuth SpielerPulse Processing and Analysis LBNL

4

A Typical Detector System – Scintillation Detector

Processes in Scintillator – Photomultiplier

number of photons number of photoelectrons charge in pulse∝ absorbed energy ∝ absorbed energy ∝ abs. energy

Signal Processing

charge in pulse pulse height∝ abs. energy ∝ absorbed energy

SCINTILLATOR PHOTOMULTIPLIER

CURRENTPULSE

INCIDENT RADIATION

INCIDENT RADIATION

SCINTILLATOR PHOTOCATHODE ELECTRONMULTIPLIER

LIGHT ELECTRONS ELECTRICALSIGNAL

PHOTOMULTIPLIER

PULSE SHAPING ANALOG TO DIGITAL CONVERSION

DIGITALDATA BUS

2002 IEEE Short Course Radiation Detection and Measurement Helmuth SpielerPulse Processing and Analysis LBNL

4

A Typical Detector System – Scintillation Detector

Processes in Scintillator – Photomultiplier

number of photons number of photoelectrons charge in pulse∝ absorbed energy ∝ absorbed energy ∝ abs. energy

Signal Processing

charge in pulse pulse height∝ abs. energy ∝ absorbed energy

SCINTILLATOR PHOTOMULTIPLIER

CURRENTPULSE

INCIDENT RADIATION

INCIDENT RADIATION

SCINTILLATOR PHOTOCATHODE ELECTRONMULTIPLIER

LIGHT ELECTRONS ELECTRICALSIGNAL

PHOTOMULTIPLIER

PULSE SHAPING ANALOG TO DIGITAL CONVERSION

DIGITALDATA BUS

μ

5” PMT

ν νe

Scintillation signals

Stopped Muon Electron

Detector this scintillation light (in the visible, mostly) with a

“photo-multiplier tube,” PMT,

or a

“Silicon Photo Multiplier,” SiPM

or … photo-diode, photo-triode, etc.

PMT (Photomultiplier tubes)

▲ Photomultiplier Tubes

▲ Photomultiplier Tube Modules

Electron Optics of Photomultipliers

FRONT- END REGION

Fig. 26 Photomultiplier design with curved faceplate and in-line dynode structure toprovide a minimum transit time and transit-time spread.

PHOTOCATHODE

DYNODE NO. I

TYPICALELECTRONTRAJECTORIES

TYPICALEQUIPOTENTIALLINES

Fig. 27 Cross section of a photomultiplier showing equipotential lines and electrontrajectories that were plotted by computer.

31

Event Information

• body0: ADC counts of the early signal

• body: ADC counts of the late signal

• dt: time difference between two signal peaks

Mean Lifetime for Particle DecayThe probability for decay

The probability that a particle will remain at time t

The mean lifetime

=1/λ

From the experiment, can you:

• see the muon and electron signals with the oscilloscope?

• draw signal distributions of the muons and electrons in ADC counts?

• make a plot for the time difference between two signal peaks?

• obtain the mean lifetime of muons by fitting the plot obtained in the previous step?